I’ve got a Lister D to tinker with, pretty much the Ford Focus of the stationary engine world.
You need to decide if you want a fixer upper or a runner. Recalling that the fun comes from their simplicity and the ability for you to fix easily. Buying a good one just to run might get boring after a while unless you have invested time getting it running.
Having it mounted on a wheeled trolley is pretty much compulsory. They weigh a lot. It sounds like you should be searching for an engine plus pump mounted as a unit on a trolley.
As these engines are old they have often been re-bored. That can only be done so often, not just because of thickness of the bore walls, but also because of the maximum oversize available pistons and rings. Worth asking the vendor.
Make sure the oil used is SAE30 or similar, modern oils that are designed to keep foreign particles in suspension (until they get to the oil filter) don’t work in a splash lubrication system with no filter. Particles need to settle out.
I suggest something with an open crank for maximum injury potential.